We introduce a generalization of the Gorenstein injective modules: the Gorenstein FP n-
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …

Over any associative ring $ R $ it is standard to derive $\mathrm {Hom} _R (-,-) $ using
projective resolutions in the first variable, or injective resolutions in the second variable, and …

In this paper, we study the relative homological dimension based on the class of projectively
coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and …

We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

Let R be a commutative ring. We show that any complete duality pair gives rise to a theory of
relative homological algebra, analogous to Gorenstein homological algebra. Indeed …

We study homotopy categories of model categories arising from a cotorsion triple, and the
equivalences between corresponding stable categories. We characterize homological …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

Let R be a general ring. Duality pairs of R-modules were introduced by Holm-Jørgensen.
Most examples satisfy further properties making them what we call semi-complete duality …

We introduce the notion of balanced pair of additive subcategories in an abelian category.
We give sufficient conditions under which a balanced pair of subcategories gives rise to a …

In this article, we study the relation between m-strongly Gorenstein projective (resp.,
injective) modules and n-strongly Gorenstein projective (resp., injective) modules whenever …